A new measure of node centrality on schedule-based space-time networks for the designation of spread potential

Abstract

Node centrality is one of the most frequently revisited network theoretical concepts, which got many calculation method alternatives, each of them being conceived on different empirical or theoretical network abstractions. The vast majority of centrality measures produced up to date were conceived on static network abstractions (the so-called "snapshot" networks), which arguably are less realistic than dynamic (temporal) network abstractions. The new, temporal node centrality measure that we offer with this article, is based on an uncommon abstraction, of a space-time network derived from service schedules (timetables). The proposed measure was designed to rank nodes of a space-time network based on their spread or transmission potential, and was subsequently implemented on the network of sea ferry transportation derived from the aggregated schedules for sea ferry liner shipping services in Europe, as they occurred in the month of August, 2015. The main feature of our measure, named "the Spread Potential", is the evaluation of the potential of a node in the network for transmitting disease, information (e.g. rumours or false news), as well as other phenomena, whichever support a space-time network abstraction from regular and scheduled services with some known carrying capacities. Such abstractions are, for instance, of the transportation networks (e.g. of airline or maritime shipping or the wider logistics (delivery) networks), networks of medical (hospital) services, educational (teaching) services, and virtually, of any other scheduled networked phenomenon. The article also offers the perspectives of the measure's applicability on the non-scheduled space-time network abstractions.

A new measure of node centrality on schedule-based space-time networks for the designation of spread potential

“…These providers offered over 200 different routes altogether, spanning across more than 100 ports. The dataset, comprising consolidated schedules, including web-links from which the schedules were retrieved, is available as Supplementary Data 40 . Data on the ships’ capacities deployed on each route (path) were not available for most routes; we have instead collected the data on maritime distances (in nautical miles) between ports ( ), using some free online web services, such as https://sea-distances.org/ .…”

“…In Table 1 , in the leftmost numeric column (SP-B) we provide the spread potential (SP) values for the top-30 (of, in total, 125) ports, sorted in descending order by SP values when applied in a binary network abstraction, that is, in which all weights on crossing links were set to equal 1 before algorithm’s execution. The full ranking of ports is available as the Supplementary Data 40 . Column SP-W shows the results of our algorithm run on a weighted network abstraction, in which the distance-proxied capacities were assigned on the crossing links.…”

“…We have run the two measures as in their original (binary) formulation, but we also made an extension to the metrics to incorporate link weights (TD-W and TC-W), in the generalization as proposed by 44 , which also is referred to in 35 . Our results (indicator rankings) are provided along with the previously discussed static metrics in the Supplementary material 40 with the according headers (TD-B, TC-B, TD-W, TC-W).…”

“…The datasets generated and/or analysed during the current study are available in the Figshare repository referred to and cited in the document as Supplementary Data 40 .…”